Objectives: Improve and extend mathematical models for the distribution and disposition of drugs, environmental contaminants and endogenous metabolites in animals and man to: (1) Account for species differences in drug distribution. (2) Provide rational bases for extrapolation of toxicity from animals to man. (3) In conjuction with pharmacodynamics, provide a basis for optimization of cancer chemotherapy and chronic hemodialysis. (4) Enable rational transfer of in vitro thermodynamic and kinetic data to in vivo cases. (5) Predict effective dose schedules of anti-cancer drugs in individual patients. Methods employed: Mathematical models are developed from physicochemical, physiological and anatomical information and the principles of chemical reaction engineering. Resulting differential equations sets are solved analytically or numerically and compared with experimental data. Uncertainties are clarified by additional experiments and model modification. Major findings: (1) Methotrexate distribution in spontaneous canine lymphosarcoma has been modeled as a saturable transport process with strong intracellular binding to dihydrofolate reductase and weak binding to cell membranes or extracellular tumor components. (2) A pharmacokinetic model, originally developed on the basis of extensive studies in mice, has been used successfully to predict methotrexate priming doses and infusion rates required to achieve selected plasma concentrations in individual patients. (3) Tumor perfusion, membrane transport, intracellular enzyme levels and enzyme synthesis rate have been illustrated and placed in quantitative perspective by a discussion of the pharmacokinetics and pharmacodynamics of methotrexate. This provides an operational basis for examination of drug resistance. (4) Filterability of platinum administered as cis-dichlorodiammine platinum (II) decreases during incubation with dog plasma in vitro. This appears to correlate with a decrease in kidney clearance in vivo and suggests that one or more chemical reactions occur which may influence distribution, disposition, and biological effect. Significance: Drugs and other chemicals are tested for effect in animals, and the extropolation to man is a subject of serious concern. At issue are both the risk associated with environmental contaminants and optimization of therapy.